The Ignition Index: Measuring Global Workspace Dynamics in Language Models

We introduce the Ignition Index (I), a validated scalar metric that operationalizes Global Workspace Theory's (GWT) all-or-none ignition prediction in transformer language models. The metric fits a four-parameter sigmoid to per-layer linear probe accuracy as a function of input signal strength, extracting steepness parameter beta-hat: high values indicate abrupt, ignition-like transitions; low values indicate graded build-up. Across 11 models spanning five architecture families, shuffled-label controls demonstrate 9.6-fold selectivity for genuine linguistic structure over spurious probe capacity (p < 0.001, Mann-Whitney U-test). We find: (1) Feedforward transformers exceed SSMs by 89% in aggregate beta-hat (p < 1e-13, Cohen's d = 0.52), with Mamba exhibiting near-linear profiles consistent with absent global broadcast. (2) Huginn-3.5B exhibits 2.12-fold higher ignition along its iteration axis than its depth axis, demonstrating that recurrent architectures manifest workspace-like transitions along the recurrence dimension. (3) Pythia-410M shows a PELT-detected phase transition at training step 256 (+67%), preceding induction-head formation. (4) Hypotheses linking ignition to model scale and signal strength were not confirmed, suggesting transformer architectures may saturate available ignition mechanisms. The Ignition Index provides the first validated quantitative bridge between GWT's dynamical predictions and mechanistic interpretability, with 9.6-fold measurement selectivity and architecture-level discriminability not previously characterized in the scaling literature. Code: https://github.com/saman-rahbar/ignition-index